We present a new analysis method that allows one to understand and model excited state contributions in observables that are dominated by a pion pole. We apply this method to extract axial and (induced) pseudoscalar nucleon isovector form factors, which satisfy the constraints due to the partial conservation of the axial current up to expected discretization effects. Effective field theory predicts that the leading contribution to the (induced) pseudoscalar form factor originates from an exchange of a virtual pion, and thus exhibits pion pole dominance. Using our new method, we can recover this behavior directly from lattice data. The numerical analysis is based on a large set of ensembles generated by the CLS effort, including physical pion masses, large volumes (with up to 96 3 × 192 sites and Lm π = 6.4), and lattice spacings down to 0.039 fm, which allows us to take all the relevant limits. We find that some observables are much more sensitive to the choice of parametrization of the form factors than others. On the one hand, the z-expansion leads to significantly smaller values for the axial dipole mass than the dipole ansatz (M z-exp A = 1.02(10) GeV versus M dipole A = 1.31(8) GeV). On the other hand, we find that the result for the induced pseudoscalar coupling at the muon capture point is almost independent of the choice of parametrization (g z-exp P = 8.68(45) and g dipole P = 8.30(24)), and is in good agreement with both, chiral perturbation theory predictions and experimental measurement via ordinary muon capture. We also determine the axial coupling constant g A .
Excited state contamination is one of the most challenging sources of systematics to tackle in the determination of nucleon matrix elements and form factors. The signal-to-noise problem prevents one from considering large source-sink time separations for the three-point functions to ensure ground state dominance. Instead, relevant analyses consider multi-state fits. Excited state contributions are particularly significant in the axial channel. In this work, we confront the problem directly. Since the major source of contamination is understood to be related to pion production, we consider three-point correlation functions with a nucleon operator at the source and a nucleon-pion interpolating operator at the sink, which allows studies of 𝑁 → 𝑁 𝜋 matrix elements. We discuss the construction of these three-point correlation functions and we solve the generalized eigenvalue problem (GEVP) using different sets of nucleon and nucleon-pion interpolators. The analysis is performed on the CLS ensemble A653 with 𝑚 𝜋 ≈ 420 MeV. Results were generated with valence quark masses corresponding to 𝑚 𝜋 ≈ 1750 MeV and 𝑚 𝜋 ≈ 420 MeV.
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